In a way. But initially only on the mental level.
An important and leading research has been that of the Max Planck Institute of Leipzig that analyzed the bonobo-genome in 2012. It showed 1. that we are more related to the bonobos than to the chimpanzees (for us no news) and 2. that there has been gene exchange with our close relatives up to 4.5 mya but that this has since stopped.
Of course, this last fact may have been the result of geographically separation: the bonobos remained rainforest inhabitants and the australopiths became savannah inhabitants.

But the temptation to speculate that more was going on is great. That time is close to the behavioral changes that have followed (use of fire, making stone knives and scrapers). Behavior that only can be attributed to a species that has names for the things.

Not sophistication of group animal cries! For our ANBOs, normal ape communication (cries, gestures, facial expressions and other body language) was only extended with names for the things. But those names were produced with hand gestures, not with cries.

Animals – apes are animals – have no neurological control over their voice. Animal cries are controlled by the limbic system. So the extending of their normal ape communication included facial expressions and all other body language but excluded cries.

However, our ANBOs weren’t deaf, like present-day sign language users. Their thousands and thousands of sign words were formed with silent gestures but accompanied by consonants. Consonants such as t-k-f-s-ch-p are muscle-formed, are controlled by the neocortex. To form more and more names for the things, the voiceless consonants were crucial.

So from the beginning, consonants have been part of the sign language of our ancestors.

The Singing Neanderthals of paleo Stephen Mithen (2005) were still !click-language sign language communicators in our opinion, and the oldest GH-tribes that are examples for our original GH-phase, the Hadza, the San and the Pygmies, still haven !click-languages

In the long nightly hours around the campfire, the growing gestural communication with names for the things the proto-form of sign language underwent an accelerated development towards real singing. The accompanying cries became a proto-form of singing.
Later more about the campfire and the dancing/singing.